Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu
Markus Mueller, Harvard Lars Fritz, Harvard Subir Sachdev, Harvard Markus Mueller, Harvard Lars Fritz, Harvard Subir Sachdev, Harvard Particle theorists Condensed matter theorists Sean Hartnoll, KITP Christopher Herzog, Princeton Pavel Kovtun, Victoria Dam Son, Washington Sean Hartnoll, KITP Christopher Herzog, Princeton Pavel Kovtun, Victoria Dam Son, Washington
1. CFT3s in condensed matter physics and string theory Superfluid-insulator transition, magnetic ordering transitions, graphene Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 3. Black Hole Thermodynamics Connections to quantum criticality 4. Generalized magnetohydrodynamics Quantum criticality and dyonic black holes 5. Experiments Graphene and the cuprate superconductors
1. CFT3s in condensed matter physics and string theory Superfluid-insulator transition, magnetic ordering transitions, graphene Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 3. Black Hole Thermodynamics Connections to quantum criticality 4. Generalized magnetohydrodynamics Quantum criticality and dyonic black holes 5. Experiments Graphene and the cuprate superconductors
M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
The insulator:
Excitations of the insulator:
Coupled dimer antiferromagnet
S=1/2 Heisenberg antiferromagnets on the square lattice Phase diagram or
S=1/2 Heisenberg antiferromagnets on the square lattice Algebraic spin liquids
S=1/2 Heisenberg antiferromagnets on the square lattice Algebraic charge liquids R. Kaul et al., Nature Physics 4, 28, (2008)
Graphene
1. CFT3s in condensed matter physics and string theory Superfluid-insulator transition, magnetic ordering transitions, graphene Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 3. Black Hole Thermodynamics Connections to quantum criticality 4. Generalized magnetohydrodynamics Quantum criticality and dyonic black holes 5. Experiments Graphene and the cuprate superconductors
1. CFT3s in condensed matter physics and string theory Superfluid-insulator transition, magnetic ordering transitions, graphene Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 3. Black Hole Thermodynamics Connections to quantum criticality 4. Generalized magnetohydrodynamics Quantum criticality and dyonic black holes 5. Experiments Graphene and the cuprate superconductors
Wave oscillations of the condensate (classical Gross- Pitaevski equation)
Dilute Boltzmann gas of particle and holes
CFT at T>0
D. B. Haviland, Y. Liu, and A. M. Goldman, Phys. Rev. Lett. 62, 2180 (1989) Resistivity of Bi films M. P. A. Fisher, Phys. Rev. Lett. 65, 923 (1990)
Density correlations in CFTs at T >0
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
Density correlations in CFTs at T >0 K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
1. CFT3s in condensed matter physics and string theory Superfluid-insulator transition, magnetic ordering transitions, graphene Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 3. Black Hole Thermodynamics Connections to quantum criticality 4. Generalized magnetohydrodynamics Quantum criticality and dyonic black holes 5. Experiments Graphene and the cuprate superconductors
1. CFT3s in condensed matter physics and string theory Superfluid-insulator transition, magnetic ordering transitions, graphene Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 3. Black Hole Thermodynamics Connections to quantum criticality 4. Generalized magnetohydrodynamics Quantum criticality and dyonic black holes 5. Experiments Graphene and the cuprate superconductors
Objects so massive that light is gravitationally bound to them. Black Holes
Objects so massive that light is gravitationally bound to them. Black Holes The region inside the black hole horizon is causally disconnected from the rest of the universe.
Black Hole Thermodynamics Bekenstein and Hawking discovered astonishing connections between the Einstein theory of black holes and the laws of thermodynamics
Black Hole Thermodynamics Bekenstein and Hawking discovered astonishing connections between the Einstein theory of black holes and the laws of thermodynamics
AdS/CFT correspondence The quantum theory of a black hole in a 3+1- dimensional negatively curved AdS universe is holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions Maldacena, Gubser, Klebanov, Polyakov, Witten 3+1 dimensional AdS space A 2+1 dimensional system at its quantum critical point
AdS/CFT correspondence The quantum theory of a black hole in a 3+1- dimensional negatively curved AdS universe is holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions Maldacena, Gubser, Klebanov, Polyakov, Witten 3+1 dimensional AdS space Quantum criticality in 2+1 dimensions Black hole temperature = temperature of quantum criticality
AdS/CFT correspondence The quantum theory of a black hole in a 3+1- dimensional negatively curved AdS universe is holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions Strominger, Vafa 3+1 dimensional AdS space Quantum criticality in 2+1 dimensions Black hole entropy = entropy of quantum criticality
AdS/CFT correspondence The quantum theory of a black hole in a 3+1- dimensional negatively curved AdS universe is holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions 3+1 dimensional AdS space Quantum criticality in 2+1 dimensions Quantum critical dynamics = waves in curved space Maldacena, Gubser, Klebanov, Polyakov, Witten
AdS/CFT correspondence The quantum theory of a black hole in a 3+1- dimensional negatively curved AdS universe is holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions 3+1 dimensional AdS space Quantum criticality in 2+1 dimensions Friction of quantum criticality = waves falling into black hole Son
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, (2007) Collisionless to hydrodynamic crossover of SYM3
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, (2007) Collisionless to hydrodynamic crossover of SYM3
Universal constants of SYM3 P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, (2007) C. Herzog, JHEP 0212, 026 (2002)
Electromagnetic self-duality
1. CFT3s in condensed matter physics and string theory Superfluid-insulator transition, magnetic ordering transitions, graphene Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 3. Black Hole Thermodynamics Connections to quantum criticality 4. Generalized magnetohydrodynamics Quantum criticality and dyonic black holes 5. Experiments Graphene and the cuprate superconductors
1. CFT3s in condensed matter physics and string theory Superfluid-insulator transition, magnetic ordering transitions, graphene Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 3. Black Hole Thermodynamics Connections to quantum criticality 4. Generalized magnetohydrodynamics Quantum criticality and dyonic black holes 5. Experiments Graphene and the cuprate superconductors
For experimental applications, we must move away from the ideal CFT e.g. A chemical potential A magnetic field B CFT
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
Conservation laws/equations of motion S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
Constitutive relations which follow from Lorentz transformation to moving frame S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
Single dissipative term allowed by requirement of positive entropy production. There is only one independent transport co-efficient S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
For experimental applications, we must move away from the ideal CFT e.g. A chemical potential A magnetic field B An impurity scattering rate 1/ imp (its T dependence follows from scaling arguments) CFT
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
Solve initial value problem and relate results to response functions (Kadanoff+Martin)
From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
To the solvable supersymmetric, Yang-Mills theory CFT, we add A chemical potential A magnetic field B After the AdS/CFT mapping, we obtain the Einstein-Maxwell theory of a black hole with An electric charge A magnetic charge The exact results are found to be in precise accord with all hydrodynamic results presented earlier S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007) Exact Results
Solve quantum Boltzmann equation for graphene The results are found to be in precise accord with all hydrodynamic results presented earlier, and many results are extended beyond hydrodynamic regime. M. Müller, L. Fritz, and S. Sachdev, arXiv:
Collisionless-hydrodynamic crossover in pure, undoped, graphene L. Fritz, M. Mueller, J. Schmalian and S. Sachdev, arXiv: See also A. Kashuba, arXiv: I. Herbut, V. Juricic, and O. Vafek, Phys. Rev. Lett. 100, (2008).
1. CFT3s in condensed matter physics and string theory Superfluid-insulator transition, magnetic ordering transitions, graphene Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 3. Black Hole Thermodynamics Connections to quantum criticality 4. Generalized magnetohydrodynamics Quantum criticality and dyonic black holes 5. Experiments Graphene and the cuprate superconductors
1. CFT3s in condensed matter physics and string theory Superfluid-insulator transition, magnetic ordering transitions, graphene Quantum-critical transport Collisionless-t0-hydrodynamic crossover of CFT3s 3. Black Hole Thermodynamics Connections to quantum criticality 4. Generalized magnetohydrodynamics Quantum criticality and dyonic black holes 5. Experiments Graphene and the cuprate superconductors
Dirac fermions in graphene Tight binding dispersion Honeycomb lattice of C atoms Close to the two Fermi points K, K’: 2 relativistic (Dirac) cones in the Brillouin zone Coulomb interactions: Fine structure constant “Speed of light”
Phase diagram & Quantum criticality
J.-H. Chen et al. Nat. Phys. 4, 377 (2008).
Universal conductivity Q : graphene L. Fritz, J. Schmalian, M. Mueller, and S. Sachdev, arXiv: General doping: Clean system: Will appear in all Boltzmann formulae below! Gradual disappearance of quantum criticality and relativistic physics
Universal conductivity Q : graphene General doping: Lightly disordered system: L. Fritz, J. Schmalian, M. Mueller, and S. Sachdev, arXiv:
Universal conductivity Q : graphene General doping: Lightly disordered system: Fermi liquid regime: L. Fritz, J. Schmalian, M. Mueller, and S. Sachdev, arXiv:
Universal conductivity Q : graphene General doping: Lightly disordered system: Fermi liquid regime: Maryland group (‘08): Graphene J.-H. Chen et al. Nat. Phys. 4, 377 (2008). L. Fritz, J. Schmalian, M. Mueller, and S. Sachdev, arXiv:
Cyclotron resonance in graphene Conditions to observe resonance Negligible Landau quantization Hydrodynamic, collison-dominated regime Negligible broadening Relativistic, quantum critical regime } M. Mueller, and S. Sachdev, arXiv:
Proposed phase diagram for cuprates QCP
Nernst measurements QCP
Nernst experiment Vortices move in a temperature gradient Phase slip generates Josephson voltage 2eV J = 2 h n V E J = B x v H eyey HmHm Nernst signal e y = E y /| T |
From these relations, we obtained results for the transport co-efficients, expressed in terms of a “cyclotron” frequency and damping: S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B (2007)
LSCO Experiments Measurement of (T small) Y. Wang et al., Phys. Rev. B 73, (2006).
LSCO Experiments Measurement of (T small) Y. Wang et al., Phys. Rev. B 73, (2006).
87 LSCO Experiments Measurement of (T small) Y. Wang et al., Phys. Rev. B 73, (2006). T-dependent cyclotron frequency! times smaller than the cyclotron frequency of free electrons (at T=35 K) Only observable in ultra-pure samples where. → Prediction for c :
Theory for LSCO Experiments Y. Wang, L. Li, and N. P. Ong, Phys. Rev. B 73, (2006). -dependence
Y. Wang, L. Li, and N. P. Ong, Phys. Rev. B 73, (2006). Theory for LSCO Experiments
Theory for transport near quantum phase transitions in superfluids and antiferromagnets Exact solutions via black hole mapping have yielded first exact results for transport co- efficients in interacting many-body systems, and were valuable in determining general structure of hydrodynamics. Theory of Nernst effect near the superfluid- insulator transition, and connection to cuprates. Quantum-critical magnetotransport in graphene. Theory for transport near quantum phase transitions in superfluids and antiferromagnets Exact solutions via black hole mapping have yielded first exact results for transport co- efficients in interacting many-body systems, and were valuable in determining general structure of hydrodynamics. Theory of Nernst effect near the superfluid- insulator transition, and connection to cuprates. Quantum-critical magnetotransport in graphene. Conclusions